
Interestingly, it has been later shown that, the provided lower bound here still is not tight, and there is still room to further improvement.
Therefore, in the paper [1]} have shown that the bound given here could be further optimized, such that selecting \(\Vert  \Omega \Vert \)  just to be lower bounded by \(8 r \mu _0 \log { \frac{r}{\epsilon }}\)  is enough for the algorithm.
